The number of points in $(-\infty, \infty)$,for which $x^2-x \sin x-\cos x=0$,is

When a non-volatile solute is added to a solvent,the vapor pressure decreases by $10 \ mm$. The mole fraction of the solute is $0.2$. If the vapor pressure decreases by $20 \ mm$,what will be the mole fraction of the solvent?

$K_1, K_2$ and $K_3$ are the equilibrium constants of the following reactions $(I), (II)$ and $(III)$,respectively :
$(I) \ N_2 + 2O_2 \rightleftharpoons 2NO_2$
$(II) \ 2NO_2 \rightleftharpoons N_2 + 2O_2$
$(III) \ NO_2 \rightleftharpoons \frac{1}{2}N_2 + O_2$
The correct relation from the following is

In a first order reaction,the concentration of the reactant decreases from $0.6 \ M$ to $0.3 \ M$ in $15 \ min$. The time taken for the concentration to change from $0.1 \ M$ to $0.025 \ M$ in minutes is

$A$ steel meter scale is to be ruled so that millimeter intervals are accurate within about $5 \times 10^{-5} \ m$ at a certain temperature. The maximum temperature variation allowable during the ruling is (Coefficient of linear expansion of steel $= 10 \times 10^{-6} \ K^{-1}$) (in $^{\circ} C$)

The pressure versus temperature graph of an ideal gas for equal number of moles at different volumes is plotted as shown in the figure. Choose the correct alternative.